Gavin Jones's friend is planning to invest $ I million in a rock concert to be held I year from noW The friend figures that he will obtain $3 million revenue from his $1 million investment-unless, my goodness, it rains If it rains, he will lose his entire investment There is a 50% chance that it will rain the day of the concert Gavin suggests that he buy rain insurance He can buy one unit of insurance for $ 50, and this unit pays $1 if it rains and nothing if it does not He may pUlchase as many units llS he wishes. up to $3 million

Required:
a. What is the expected rate of return on his investment if he buys units of insurance?
b. What number of units will minimize the variance of his return? What is this minimunm value? And what is the corresponding expected rate of return?

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jepessoa jepessoa · Answer 1 · 2020-10-12T18:40:53+02:00

Answer:

a. What is the expected rate of return on his investment if he buys u units of insurance?

total cost = $1,000,000 (concert cost) + $0.50u

return if it rains = $0 + $u

expected return:

doesn't rain = ($3,000,000 x 50%) = $1,500,000

rains = $0 + $u

expected rate of return = [($1,500,000 + $u) / ($1,000,000 + $0.5u)] - 1

b. What number of units will minimize the variance of his return? What is this minimum value? And what is the corresponding expected rate of return?

if you buy 3,000,000 units of u then variance is 0. Whether it rains or not, expected revenue = $3,000,000

total costs = $1 million (concert cost) + ($0.50 x 3 million units of insurance purchased) = $2,500,000

rate of return = ($3,000,000 / $2,500,000) - 1 = 20%